Dilatancy (granular material)In soil mechanics, dilatancy is the volume change observed in granular materials when they are subjected to shear deformations. This effect was first described scientifically by Osborne Reynolds in 1885/1886 and is also known as Reynolds dilatancy. It was brought into the field of geotechnical engineering by Peter Walter Rowe. Unlike most other solid materials, the tendency of a compacted dense granular material is to dilate (expand in volume) as it is sheared.
Three-body forceA three-body force is a force that does not exist in a system of two objects but appears in a three-body system. In general, if the behaviour of a system of more than two objects cannot be described by the two-body interactions between all possible pairs, as a first approximation, the deviation is mainly due to a three-body force. The fundamental strong interaction does exhibit such behaviour, the most important example being the stability experimentally observed for the helium-3 isotope, which can be described as a 3-body quantum cluster entity of two protons and one neutron [PNP] in stable superposition.
Mean squared displacementIn statistical mechanics, the mean squared displacement (MSD, also mean square displacement, average squared displacement, or mean square fluctuation) is a measure of the deviation of the position of a particle with respect to a reference position over time. It is the most common measure of the spatial extent of random motion, and can be thought of as measuring the portion of the system "explored" by the random walker.
Entropic forceIn physics, an entropic force acting in a system is an emergent phenomenon resulting from the entire system's statistical tendency to increase its entropy, rather than from a particular underlying force on the atomic scale. In the canonical ensemble, the entropic force associated to a macrostate partition is given by where is the temperature, is the entropy associated to the macrostate , and is the present macrostate.
Functional integrationFunctional integration is a collection of results in mathematics and physics where the domain of an integral is no longer a region of space, but a space of functions. Functional integrals arise in probability, in the study of partial differential equations, and in the path integral approach to the quantum mechanics of particles and fields. In an ordinary integral (in the sense of Lebesgue integration) there is a function to be integrated (the integrand) and a region of space over which to integrate the function (the domain of integration).
Self-categorization theorySelf-categorization theory is a theory in social psychology that describes the circumstances under which a person will perceive collections of people (including themselves) as a group, as well as the consequences of perceiving people in group terms. Although the theory is often introduced as an explanation of psychological group formation (which was one of its early goals), it is more accurately thought of as general analysis of the functioning of categorization processes in social perception and interaction that speaks to issues of individual identity as much as group phenomena.
Correlated equilibriumIn game theory, a correlated equilibrium is a solution concept that is more general than the well known Nash equilibrium. It was first discussed by mathematician Robert Aumann in 1974. The idea is that each player chooses their action according to their private observation of the value of the same public signal. A strategy assigns an action to every possible observation a player can make. If no player would want to deviate from their strategy (assuming the others also don't deviate), the distribution from which the signals are drawn is called a correlated equilibrium.
